Effects of Lewis and Karlovitz numbers on transport equations for turbulent kinetic energy and enstrophy  

Lewis数和Karlovitz数对湍流动能和拟能输运方程的影响

作　　者：Hsu-Chew Lee Xiaoyu Liu Peng Dai Zheng Chen Abouelmagd Abdelsamie Minping Wan 李树洲;刘晓宇;戴鹏;陈正;Abouelmagd Abdelsamie;万敏平(Guangdong Provincial Key Laboratory of Turbulence Research and Applications,Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,518055,China;Department of Mechanics and Engineering Science,College of Engineering,Peking University,Beijing,100871,China;Laboratory of Fluid Dynamics and Technical Flows,University of Magdeburg“Otto von Guericke”,Magdeburg,39106,Germany;National Center for Applied Mathematics Shenzhen,Shenzhen,518055,China)

机构地区：[1]Guangdong Provincial Key Laboratory of Turbulence Research and Applications,Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,518055,China [2]Department of Mechanics and Engineering Science,College of Engineering,Peking University,Beijing,100871,China [3]Laboratory of Fluid Dynamics and Technical Flows,University of Magdeburg“Otto von Guericke”,Magdeburg,39106,Germany [4]National Center for Applied Mathematics Shenzhen,Shenzhen,518055,China

出　　处：《Acta Mechanica Sinica》2022年第7期29-44,I0001,共17页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.91752201 and 11672123);Shenzhen Science and Technology Program(Grant Nos.JCYJ20170412151759222,JCYJ20180302173952945,and KQTD20180411143441009);Department of Science and Technology of Guangdong Province(Grant No.2019B21203001);Project No.LCH-2019011 under the Joint Program of Shenzhen Clean Energy Research Institute and SUSTech through contract CERI-KY-2019-003.

摘　　要：A three-dimensional Direct numerical simulation(DNS)with complex chemistry was employed to examine the statistical behavior of turbulent kinetic energy(TKE)and enstrophy transport equations in hydrogen(Lewis number(Le)≈0.4)and dodecane(Le≈4.2)flames.The Karlovitz(Ka)numbers ranged from 4 to 150,involving both the thin and broken reaction zones.Budget analyses of TKE and enstrophy transport equations are performed,and scaling terms in the literature are re-examined.Similar to thin reaction zone flames,viscous dissipation term appears to be the most important term in the TKE balance,while viscous dissipation and vortex-stretching terms are the dominant terms in the enstrophy transport equation at high Ka number.The velocity-pressure gradient and the mean velocity dilatation in the TKE transport equation and the dilatation term in enstrophy budget are found to be affected by the Le.Modified scaling estimations for those terms affected by Le are proposed in this work to account for the Le effects spanning different combustion regimes.This work confirmed that Kolmogorov’s first hypothesis is not valid for low Ka number flames investigated in this study,where the vortex stretching and viscous dissipation terms cannot be scaled with local dissipation and viscosity.At sufficiently high Ka number flames,the vorticity can be scaled with the Kolmogorov time scale,and the mean enstrophy value approaches homogeneous,isotropic,non-reacting turbulence flow,but lower Le fuels require much higher Ka number to achieve that.本文通过考虑复杂化学的三维直接数值模拟(DNS),研究了氢火焰(Lewis数约为0.4)和十二烷火焰(Lewis数约为4.2)中的湍动能(TKE)与拟涡能输运方程的统计行为.算例中,Karlovitz(Ka)数在4到150之间,涉及薄反应区和破碎反应区.对湍动能与拟涡能输运方程进行了收支分析,并重新验证了过往文献中的标度项.高Ka数下,粘性耗散项是湍动能平衡中最重要的项,而拟涡能输运方程中的主导项则是粘性耗散项与涡拉伸项,这一性质与薄反应区火焰相似.湍动能输运方程中的速度-压强梯度项和平均速度膨胀项,以及拟涡能输运方程中的膨胀项则受Lewis数的影响.本文提出了受Lewis数影响项的修正标度估计,以解释不同燃烧状态下的Lewis数效应.这项工作表明,Kolmogorov的第一假设并不适用于本文所研究的低Ka数火焰,这类火焰中涡拉伸项与粘性耗散项并不与局部耗散率与粘性呈比例关系.当Ka数足够高时,涡量可以用Kolmogorov时间尺度来衡量,平均拟涡能值接近均匀各向同性的非反应湍流,但较低的Lewis数的燃料需要更高的Ka数才能实现这一点.

关 键 词：Direct numerical simulations Turbulent premixed flames Lewis number Complex chemistry 

分 类 号：O3[理学—力学] O17